Model selection and parameter estimation for dynamic epidemic models via iterated filtering: application to rotavirus in Germany

Abstract

Despite the wide application of dynamic models in infectious disease epidemiology, the particular modeling of variability in the different model components is often subjective rather than the result of a thorough model selection process. This is in part because inference for a stochastic transmission model can be difficult since the likelihood is often intractable due to partial observability. In this work, we address the question of adequate inclusion of variability by demonstrating a systematic approach for model selection and parameter inference for dynamic epidemic models. For this, we perform inference for six partially observed Markov process models, which assume the same underlying transmission dynamics, but differ with respect to the amount of variability they allow for. The inference framework for the stochastic transmission models is provided by iterated filtering methods, which are readily implemented in the R package pomp by King and others (2016, Statistical inference for partially observed Markov processes via the R package pomp. Journal of Statistical Software69, 1-43). We illustrate our approach on German rotavirus surveillance data from 2001 to 2008, discuss practical difficulties of the methods used and calculate a model based estimate for the basic reproduction number $R_0$ using these data.

Rational evaluation of various epidemic models based on the COVID-19 data of China

“…Since the accurate epidemic forecast is so critical, there are diverse methods reported in the literature to try to achieve this goal [8][9][10][11][12] . Among them, empirical functions, methods based on statistical inference and dynamical models (difference equations, ODEs and PDEs) are three major routines (see Fig.…”

Iterated Filtering Methods for Markov Process Epidemic Models

“…After presenting a simple toy example as a proof of concept, we now give a short illustration of a real-world problem which accommodates some of the complications presented in the previous section and was analyzed with iterated filtering. A detailed description of the model and inference results can be found in Stocks et al (2018). The data which were analyzed in that paper are the weekly reported number of new laboratory-confirmed rotavirus cases among children, adults and elderly from 2001 until 2008 in Germany, scaled up by an underreporting rate (cf.…”

“…assess the effect of vaccination campaigns or other public health control measures. In Stocks et al (2018) the disease transmission was modeled as an agestratified SIRS Markov process with overdispersion in the observation (cf.…”

“…Further implementational details for this example are available at Stocks (2017). The aim of the analysis in Stocks et al (2018) was to compare the impact of different kinds of variabilities in the transmission as well as the observation model. The paper concluded that a model which accounts for overdispersion in both model components (dark and light shading in Figure 1.5) is best suited to explain the analyzed data.…”

“…The package has already been applied to answer many different epidemiological questions for different infectious diseases, e.g. for cholera (King et al, 2008), measles (He et al, 2010), malaria (Bhadra et al, 2011), polio (Martinez-Bakker et al, 2015), ebola (King et al, 2015a), and rotavirus (Martinez et al, 2016;Stocks et al, 2018). Finally, iterated filtering has facilitated the development and analysis of a divers array of mechanistic models, a recent and comprehensive review of which can be found in Bretó (2017).…”